where the temperature rises δ 2 andδ 3 are those measured at timet C(1,3). The smallest sap velocity at which Eqn.14 applies depends on the probe spacing and recording time, which limit the range of sap velocities that can be measured using the CHPM (Eqn. 11 ). For example, for our recording time (400 s after the heat pulse) and probe spacing (1.5 cm between Probe #1 and #3), the lowest sap velocity that could be inferred from Eqn.11 would correspond with the temperature rises of Probe #1 and #3 crossing over 400 s after the heat pulse, giving V = (x 1 +x 3)/2t = (-0.75 + 2.25)/(2⋅400)= 1.88⋅10-3 cm s-1, or 6.75 cm h-1. The maximumV at which Eqn. 14 applies depends on theσ T, Q and mc . Fig. 2 illustrates how the maximum discernible sap velocity varies with mc for various settings of probe and heat parameters (Table S1 ). The drier the sapwood, the broader the range of velocities to which Eqn.14 applies because smaller mc leads to larger k .
We estimate k as follows. First, we use Eqn. 13 to estimate k prior to dawn, when sap velocity can be assumed to be zero. We apply that value of k until V rises high enough (e.g. > 6.75 cm h-1) in the early mornings for us to calculate k from Eqn. 14 . WhenV exceeds the range in which Eqn. 14 is applicable (e.g., 50 cm h-1 in Fig. 2a ), we use the last estimated value of k until V falls again into a range in which Eqn. 14 can be applied.